Modelling Hydrometeorological Extremes Associated to the Moisture Transport Driven by the Great Plains Low-Level Jet

The Great Plains Low-Level Jet system consists of very strong winds in the lower troposphere that transport a huge amount of moisture from the Gulf of Mexico to the American Great Plains. This paper aims to study the extremes of the Transported Moisture (TM) from the GPLLJ source region to the jet domain; and, for low and high TM, to analyze the extremal dependence between the upper tail of the precipitation in the GPLLJ sink region and the lower tail of the tropospheric stability in that region (omega). The declustered extremes of TM were analyzed using Peaks Over Threshold (POT). A non-stationary Exponential model was fitted to the cluster maxima. Estimated return levels show that the extremes of TM are expected to decrease in the future. This is meteorologically congruent with the known displacement of the western edge of the North Atlantic Subtropical High, which controls atmospheric circulation in the North Atlantic, and to a higher scale with the change of phase from negative to positive of the Atlantic Multidecadal Oscillation. Bilogistic and Logistic models were fitted to the extremes of (-omega, precipitation) for low and high TM, respectively. The extremal dependence between "-omega" and precipitation proves to be stronger in the case of high TM. This confirms that dynamical instability represented by “-omega” is the most important parameter for achieving high values of precipitation once there is a mechanism that allows the continuous supply of large amounts of moisture, such as the derived from a low-level jet system.

ON THE EXTREMAL DEPENDENCE COEFFICIENTS OF GAUSSIAN DISTRIBUTIONS

The paper considers a way to represent the relationship between indicators in the form of copulas. Copulas are popular mathematical tools. This is due to the fact that, on the one hand, the marginal distributions of indicators are divided in the copulas, and on the other hand, the structure of the relationship between these marginal distributions is divided, which makes it possible to very effectively study the connections that arise in real populations. Special attention in the work is paid to extremal dependence coefficients - important numerical characteristics of the connection in conditions of extreme small or extremely large values of indicators. It is shown that even under conditions of close correlation between the indices for a two-dimensional Gaussian distribution, the lower and upper coefficients of the extreme dependence take zero values. This indicates the impossibility of predicting the values of one indicator when fixing too small or too large values of another indicator. This work shows that the relationship between the number of COVID-19 coronavirus infections per 100,000 people and the number of deaths from COVID-19 coronavirus infection per 100,000 people in the regions of the Russian Federation can be represented in the form of a Gaussian copula.

Significant Extremal Dependence of a Daily North Atlantic Oscillation Index (NAOI) and Weighted Regionalised Rainfall in a Small Island Using the Extremogram

Extremal dependence or independence may occur among the components of univariate or bivariate random vectors. Assessing which asymptotic regime occurs and also its extent are crucial tasks when such vectors are used as statistical models for risk assessment in the field of Climatology under climate change conditions. Motivated by the poor resolution of current global climate models in North Atlantic Small Islands, the extremal dependence between a North Atlantic Oscillation index (NAOI) and rainfall was considered at multi-year dominance of negative and positive NAOI, i.e., −NAOI and +NAOI dominance subperiods, respectively. The datasets used (from 1948–2017) were daily NAOI, and three daily weighted regionalised rainfall series computed based on factor analysis and the Voronoi polygons method from 40 rain gauges in the small island of Madeira (∼740 km2), Portugal. The extremogram technique was applied for measuring the extremal dependence within the NAOI univariate series. The cross-extremogram determined the dependence between the upper tail of the weighted regionalised rainfalls, and the upper and lower tails of daily NAOI. Throughout the 70-year period, the results suggest systematic evidence of statistical dependence over Madeira between exceptionally −NAOI records and extreme rainfalls, which is stronger in the −NAOI dominance subperiods. The extremal dependence for +NAOI records is only significant in recent years, however, with a still unclear +NAOI dominance.

A regionalisation approach for rainfall based on extremal dependence

To mitigate the risk posed by extreme rainfall events, we require statistical models that reliably capture extremes in continuous space with dependence. However, assuming a stationary dependence structure in such models is often erroneous, particularly over large geographical domains. Furthermore, there are limitations on the ability to fit existing models, such as max-stable processes, to a large number of locations. To address these modelling challenges, we present a regionalisation method that partitions stations into regions of similar extremal dependence using clustering. To demonstrate our regionalisation approach, we consider a study region of Australia and discuss the results with respect to known climate and topographic features. To visualise and evaluate the effectiveness of the partitioning, we fit max-stable models to each of the regions. This work serves as a prelude to how one might consider undertaking a project where spatial dependence is non-stationary and is modelled on a large geographical scale.

Regional frequency analysis of extreme storm surges using the extremogram approach

To withstand coastal flooding, protection of coastal facilities and structures must be designed with the most accurate estimate of extreme storm surge return levels (SSRLs). However, because of the paucity of data, local statistical analyses often lead to poor frequency estimations. The regional frequency analysis (RFA) reduces the uncertainties associated with these estimations by extending the dataset from local (only available data at the target site) to regional (data at all the neighboring sites including the target site) and by assuming, at the scale of a region, a similar extremal behavior. In this work, the empirical spatial extremogram (ESE) approach is used. This is a graph representing all the coefficients of extremal dependence between a given target site and all the other sites in the whole region. It allows quantifying the pairwise closeness between sites based on the extremal dependence. The ESE approach, which should help with have more confidence in the physical homogeneity of the region of interest, is applied on a database of extreme skew storm surges (SSSs) and used to perform a RFA.

Determining the dependence structure of multivariate extremes

Summary In multivariate extreme value analysis, the nature of the extremal dependence between variables should be considered when selecting appropriate statistical models. Interest often lies in determining which subsets of variables can take their largest values simultaneously while the others are of smaller order. Our approach to this problem exploits hidden regular variation properties on a collection of nonstandard cones, and provides a new set of indices that reveal aspects of the extremal dependence structure not available through existing measures of dependence. We derive theoretical properties of these indices, demonstrate their utility through a series of examples, and develop methods of inference that also estimate the proportion of extremal mass associated with each cone. We apply the methods to river flows in the U.K., estimating the probabilities of different subsets of sites being large simultaneously.